Universal Knuckle Deadlock (Gimbal Lock)

There are a lot of articles on the deadlock of universal joints, but the writing is more cumbersome, this problem only need to know a concept.

In robotics This problem is generally referred to as the Kinetic singularity (Kinematic singularity). 1, you can see the connection axis has three rotating joints, rotating Joint 1 is around the X6 axis rotation, rotating Joint 2 is around the Y6 axis rotation, rotating Joint 3 is around Z6 axis of rotation. We can now treat three rotating joints as a whole, which is equivalent to the wrist, because the wrist is three degrees of freedom. So why call this kinetic singularity? We make a small change, we rotate the entire structure around the Y6 axis outward 90 degrees. This time the swivel joint 1 and the swivel Joint 2 are in a straight line, and theX6 and Z6 are coincident. This happens because we lose a degree of freedom, we can only rotate around the X6 axis or Y6 axis at this time, and theZ6 axis "disappears".

Figure 1

The following is a description of the situation in graphic science. 2, we first rotate the coordinate system around the z -axis 30 degrees, then rotate around the y -axis 90 degrees, and then rotate around the x -axis 40 degrees (the direction of the map is identified), and finally get the rightmost red coordinates. We record the whole process as (30,90,-40). Then we can see that we just rotate 70 degrees around the z axis and then rotate 90 degrees around the Y axis to achieve the final side effect. We write this process down as (70,90,0). So why (30,90,-40) = (70,90,0)? This looks like a two-way location, and it's not too much of a problem. But the careful person can find that this is actually the same as the dynamics singularity in the robotics study above. I used three degrees of freedom to complete the rotation with two degrees of freedom can be completed. After all, it is because we rotated a 90 degree, so that the x -axis and z -axis coincide, resulting in degrees of freedom "disappear". This is the problem of Universal Joint deadlock . The problem is unavoidable, and a better approach is to replace Euler's angle with four of dollars .

Figure 2

Universal Joint Deadlock (Gimbal Lock)